A magic rectangle is an m× n array of the positive integers from 1 to m× n such
that the numbers in each row have a constant sum and the numbers in
each column have a constant sum (although the row sum need not equal the
column sum). Shown below is a 3 × 5 magic rectangle with the integers
Two of three arrays at left can be filled with the integers 1-24 to form a magic rectangle. Which one can't, and why not?
Let A = 1, B = 2, and so on, with each letter equal to its position in the alphabet. The lexivalue of a word is the sum of the values of its letters. For example, ROMANS has a lexivalue of 18 + 15 + 13 + 1 + 14 + 19 = 80.
Now, do the following:
For example, if you choose 11, that becomes XI in Roman numerals, and XI has a lexivalue of 24 + 9 = 33.
Are there any numbers for which the lexivalue is equal to the original number?